Description
Fracton quantum matter is characterized by excitations with constrained mobility. It remains an open challenge to identify suitable material candidates for such systems. Recently, breathing pyrochlore lattices have been argued as potential candidates for realizing fractonic constraints. Here, we study the dynamics of excitations in a toy model on such a breathing pyrochlore lattice. We show, both by analytical considerations and by numerical simulations based on cellular automaton circuit dynamics, that excitations in this model are confined to two-dimensional planes within the three-dimensional breathing pyrochlore lattice. We derive a height-field theory for the effective two-dimensional dynamics, which exhibits diffusive dynamics with slow modes at finite momenta, resulting from effective subsystem symmetries. This model, therefore, offers a potential physically realizable platform for fractonic excitations.
